Measurements
Units and Measurements If n is the numerical value and u is the unit then ; Q = nu n1u1 = n2u2 ( bigger the unit , smaller is the value ) Systems of Measurement SI MKS - meter , kilogram , seconds CGS - centimeter , gram , seconds FPS - foot , pound , seconds Fundamental Units Mass - kilogram - M Length - meter - L Time - seconds - T Temperature - Kelvin - K Current - Ampere - I/A Luminous Intensity - Candela - C Amount of Substance - mole - mol Methods of Measurement For measuring distance of stars , planets , we use the parallax method . For determining mass of planets , we use gravitational methods . For the measurement of masses of atomic species , mass spectrographs are used . For accurate measurement of time , we use atomic clocks based on the vibrations produced in a Cesium - 133 atom . Dimensional Analysis Dimensional Analysis deals with the powers to which the unit of a physical quantity is raised to . Uses of Dimensional Analysis : # To check the correctness of an equation # To find the conversion factor # To find the dimensions by comparison method Significant Figures In order to understand significant figures , we must try to understand and accept that no measurement can be accurate . For example , when the Least count of a measuring instrument is 0.01 m , it will give us accurate readings up to 0.01 m only , measurements smaller than 0.01 m cannot be measured by it . This means that no matter how small the least count of the measuring instrument is , there will always be an error of order one less up to 10-∞ . Thus , we need to decide the accuracy , which is enough to give a good idea of the quantity . For example , a person's height is 1.62 m ; but the measurement is accurate only up to 3 digits or 3 significant figures . The actual height could be 1.61927457634752641 m (even this would have an error beyond least count) .But 3 digits is enough to give a good amount of idea about a person's height . Thus , we measure it with 3 significant figures . Order of Magnitude Order of Magnitude is the power to which 10 is raised to ; to indicate the size of the quantity . Errors Personal Error Error occurring due to human errors . Random Error Error occurring due to random changes in the environment of the experiment . Systematic Error Error occurring due to a constant error in the readings of instrument . This is caused due to the faulty calibration of instrument . Instrumental Error Error occurring due to faulty construction of instrument . Error Analysis Mean Value : Average of All readings Absolute Error : Individual Reading - Mean Value Mean Absolute Error : Average of all Absolute values Relative Error : Mean Absolute Error / Mean Value Percentage Error : Relative Error x 100 1) If xn , then Error is multiplied by n 2) The errors in the measurement of two quantities are added when the two quantities are multiplied or divied . if xy ; then add the errors 3)If the quantities are added or subtracted , then the errors are added . Tips and Tricks # Use dimensional analysis to eliminate options . Try to match dimensions . Category:Physics